1. Shortcut: This door leads to the boss. Unfortunately, it's blocked off. If you want to take a shortcut, pick up a bomb and walk to the ledge. Wait until it's about to explode and then drop it. It should blow a hole in the barrier. You can then go through the door, to the boss.
2. Birdo Battle: You'll face Birdo after almost every level. To defeat him, wait until he spits out an egg and then jump onto the egg. Pick it up and toss it at him. It will only take three hits to get rid of Birdo.